Fractal as a mystical sign in Russian traditional culture

2024 Author: Seth Attwood | [email protected]. Last modified: 2023-12-16 15:55

In this article, the fractal is positioned as an archetypal model of thinking, as well as a unique sign in folk culture. The examples of fractal models in the samples of Russian traditional art are given, the analysis of which characterizes the fractal as a sign of the mystical, sacred and otherworldly.

Fractal (from Latin “fragmented”, “broken”, “irregular in shape”; the term was introduced by Benoit Mandelbrot in 1975) is a structure characterized by fracture and self-similarity; that is, composed of several parts, each of which is similar to the whole figure as a whole: "… if a part of the fractal is increased to the size of the whole, it will look like a whole, or exactly, or, perhaps, only with a slight deformation" [8, p. 40].

It is customary to associate a fractal model of self-organization with the modern scientific paradigm - synergetics, within which the general laws of the processes of transition from chaos to order and vice versa are studied. However, structures resembling fractals also figured in the forms of archaic culture (for example, in rock paintings of the megalithic era and in the ornaments of the Ancient World). It should be noted that some researchers have already drawn parallels in their works between the modern synergetic paradigm and archaic thinking.

So, Yu. V. Kirbaba in his dissertation work notes: "The origin of the synergetic paradigm, as has been repeatedly emphasized, is associated with the most ancient stages of the formation of culture. Models of self-organization were formed at the stage of the formation of mythological consciousness" [6, p.104]. It was noted that the foundations of ancient cosmogonic mythology are the origins of the principle of self-similarity, which manifests itself in three archetypal models: 1) concentric circles; 2) tree structure; 3) spiral [6].

Also M. V. Alekseeva in her article notes that "the worldview of our ancestors, expressed in ritual actions, lies in the mainstream of modern scientific ideas about the development of the universe within the framework of the theory of nonlinear systems" [1, p. 137].

Based on this, we assume that the fractal is a universal, archetypal model of thinking: "Synergetic principles and models, as it is now becoming clear, are universal categories of thinking, and therefore are reflected in the most ancient layers of human culture" [6, p.104] …

Thus, fractal constructions are also found in samples of traditional folk art: in ornaments, round dances, songs, legends, rituals, amulets, etc. Let us analyze some of the monuments of Russian folk art in order to determine the status and meanings of archetypal fractal signs in Russian traditional culture.

Fern legend

The legend of the fern can be considered an example of the emphasis on fractal structure in folk ideas. The fern is one of the clearest examples of a natural stochastic fractal. There was a popular belief that on the eve of the holiday of Ivan Kupala (summer solstice, border time) a fern blooms at night: “it shines with a fiery flame and illuminates the area; and get wealth "[3, p.78]. Here we see how a fractal structure is endowed with a special mystical status: with its help, you can unravel the mysteries of the Universe.

Divination with mirrors

The people believed that with the help of special ritual actions - fortune telling - it is possible to provoke contact with otherworldly forces, as a result of which a person learns about his future. One of the most widespread in Russian traditional culture is fortune-telling with the help of two mirrors: "they put two mirrors one against the other, … sitting between two mirrors, … looks attentively into the mirror placed in front of him" [3, p.23]. Interestingly, if we put two mirrors opposite each other, we get again a fractal, concentric image. Such a "fractal corridor", formed by the reflection of a mirror in a mirror, seemed to our ancestors a portal to the other world, which also testifies to the sacred status of the fractal form in popular beliefs.

Conspiracies

Another form of ritual interaction between the earthly and otherworldly worlds were conspiracies: “Primitive man was confident in the ability of words to act on animals and people, on natural and supernatural forces. Otherwise, the called forces either will not hear, or will not understand, or will be offended by the wrong intonation "[11, p.70]. So, in the ideas of our ancestors, conspiracies were a form of direct dialogue with otherworldly forces and were built according to certain laws. Researcher and linguist E. A. Bondarets notes that in each conspiracy the main coordinates of the "toponymic conspiracy space" are compositionally set: "On the sea, on the ocean, on an island, on a brawler, lies a white-combustible stone-Alatyr" [2, p.58]; "there is a holy okyan-stone, a red maiden sits on a holy okyan-stone …" [3, p.291]. If we represent such a space schematically, then we get concentric circles: sea-okiyan - circle 1, island-brawler - circle 2, stone-Alatyr - circle 3, red maiden - circle 4.

Lullabies

Note that many Russian folk lullabies have a concentric structure. Mukhamadieva D. M. this is how he describes the concentric structure of the figurative row of lullabies: in the center is the child himself; then mom, grandmother, father, nanny - his closest circle are placed; on the next circle there are images of domestic, friendly, kind animals (cat, goat, mouse); on the next circle there are alien, wild, evil animals (bear, wolf); on the latter - otherworldly beings (Buka, Sandman, etc.) [9]. Such a "concentric" lullaby served as a talisman for the child [7, p.253]: he is placed in the center and, as it were, surrounded by several circles inscribed in each other, which are designed to protect him from evil forces.

Ornamental embroidery

Many forms were endowed with protective meaning among the people: songs, conspiracies, ornaments, round dances, etc. The most widespread, everyday amulet was ornamental embroidery on clothes, which, according to our ancestors, was supposed to bring good luck and prosperity to its owners, to prevent the influence of evil forces: the ancient sacred meaning was passed on from generation to generation, carefully observing the “canons” "[5, p.10]. It is important that many of the oldest samples of Slavic ornamentation used in embroidery, printed fabric, wall paintings, etc. possess the properties of a fractal - self-similarity and fractional dimension. So, among the samples of traditional folk ornament presented in the book by S. I. Pisarev, we find archaic models of concentric and self-similar shaping [10]. According to M. Kachaeva, the rhythmic row of Russian traditional ornament has a spiral structure: "The structure of the rhythmic row is laid by the trajectory of the drawing … Thus, the shape of the symbol only highlights certain parts of the rhythmic row, which are nothing more than fragments of borders superimposed on each other. individual vibrations - impulses that make up the spiral "[5, p. 38].

Round dances

Fractal patterns - spirals and concentric circles - are clearly manifested in traditional folk round dances. The first type in different local traditions has a different name: cabbage, ball, snail, etc. As you might guess from the name, the pattern of such a round dance is a spiral - a shape with a fractal structure. The second type - concentric round dances - is one of the simplest and most common: people often danced in two circles, when men were in the central circle, and women were in the outer, and vice versa [4, p.28]. Thus, the round dance was a protective ornament in motion: "… round dances embrace the whole person, introducing him to the endless circulation of the Universe" [11, p.54]. That is, through the "fractal movement" our ancestors seemed to be connected with the universal laws of the universe, because the repetition and similarity characteristic of fractals are also manifested in the rhythmic repetition of natural processes (movement of heavenly bodies; change of seasons, day and night; periodicity of ebb and flow; alternation of maxima and minima of solar activity; electromagnetic waves, etc.), and in objects of nature that constantly surrounded our ancestors (trees, plants, clouds, etc.).

From the above, it follows that our ancestors attached special sacred and even mystical meaning to images that we today call fractals. The use of fractal signs was aimed at carrying out a kind of dialogue with the Universe, during which a person had to receive knowledge and apply it to preserve humanity. Perhaps our ancestors intuitively felt in fractals a certain universal law and the primary cause of world harmony.

So, in Russian traditional culture, archetypal fractal signs are associated with the categories of the otherworldly, protective, sacred and mystical.